What does it mean to say B is representing the dominant gene

Dominant genes are always represented by a capital letter which in this case is the letter B whereas recessive genes will be represented by a lower case letter like b.

You only need one copy of a dominant gene or allele to inherit it. A dominant allele is always expressed even if only one copy is present.

But you need two copies of genes or alleles to inherit the recessive gene. There also can't be a dominant allele of the gene if you are to inherit this.

Allele - Different forms of a gene